Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2016; 53(6): 1331-1345

Online first article August 25, 2016      Printed November 1, 2016

https://doi.org/10.4134/JKMS.j150499

Copyright © The Korean Mathematical Society.

$K$-g-frames and stability of $K$-g-frames in Hilbert spaces

Dingli Hua and Yongdong Huang

Beifang University of Nationalities, Beifang University of Nationalities

Abstract

A $K$-g-frame is a generalization of a g-frame. It can be used to reconstruct elements from the range of a bounded linear operator $K$ in Hilbert spaces. $K$-g-frames have a certain advantage compared with g-frames in practical applications. In this paper, the interchangeability of two g-Bessel sequences with respect to a $K$-g-frame, which is different from a g-frame, is discussed. Several construction methods of $K$-g-frames are also proposed. Finally, by means of the methods and techniques in frame theory, several results of the stability of $K$-g-frames are obtained.

Keywords: $K$-g-frame, frame, g-Bessel sequence, stability

MSC numbers: Primary 42C15, 42C40